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The Bead on a Hyperbolic Tangent model computes the dynamics if a bead constrained to slide on a hyperbolic tangent shaped wire. The model uses an Euler algorithm to evolve the system and it displays the velocity, acceleration, and normal force vectors as the bead slides along the wire. Separate graphs show the energy and force components. The goal of this teaching model is to find the proper acceleration that will guide a particle along an arbitrary single valued function, y=f(x)--in other words, to simulate the classic "bead on a wire." Although there are many methods for doing this, the focus of this work to keep the theory and procedures within the realm of freshman physics. The origins of this work are from an ongoing effort to add computation, in the form of computer animation projects, to the freshman mechanics course. This work is descdribed in the American Journal of Physics (AJP) publication "Computational problems in introductory physics: lessons from a bead on a wire," by T. Bensky and M. Moelter.

The Bead on a Hyperbolic Tangent model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the jar file will run the program if Java is installed.

Standards (2)

AAAS Benchmark Alignments (2008 Version)

4. The Physical Setting

4E. Energy Transformations

6-8: 4E/M4. Energy appears in different forms and can be transformed within a system. Motion energy is associated with the speed of an object. Thermal energy is associated with the temperature of an object. Gravitational energy is associated with the height of an object above a reference point. Elastic energy is associated with the stretching or compressing of an elastic object. Chemical energy is associated with the composition of a substance. Electrical energy is associated with an electric current in a circuit. Light energy is associated with the frequency of electromagnetic waves.

AAAS Benchmark Alignments (1993 Version)

4. THE PHYSICAL SETTING

E. Energy Transformations

4E (9-12) #2. Heat energy in a material consists of the disordered motions of its atoms or molecules. In any interactions of atoms or molecules, the statistical odds are that they will end up with less order than they began?that is, with the heat energy spread out more evenly. With huge numbers of atoms and molecules, the greater disorder is almost certain.

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